David Cameron has declared that "Britain is a Christian country and we should not be afraid to say so", in a speech to mark the 400th anniversary of the King James Bible.

Cameron told Church of England clergy gathered in Oxford that a return to Christian values could counter the country's "moral collapse" and blamed a "passive tolerance" of immoral behaviour for this summer's riots, Islamic extremism, City excess and Westminster scandals.

His words will delight traditionalists in his party and Christian groups that claim believers are increasingly marginalised .

Cameron said there were three reasons why the King James Bible was as relevant today as any point in its history.

"First, the King James Bible has bequeathed a body of language that permeates every aspect of our culture and heritage. Second, just as our language and culture is steeped in the Bible, so too is our politics.

"Third, we are a Christian country. And we should not be afraid to say so. Let me be clear: I am not in any way saying that to have another faith – or no faith – is somehow wrong.

"I know and fully respect that many people in this country do not have a religion. And I am also incredibly proud that Britain is home to many different faith communities, who do so much to make our country stronger. But what I am saying is that the Bible has helped to give Britain a set of values and morals which make Britain what it is today."

Cameron added that while faith was neither a "necessary nor sufficient condition for morality" it could be a "helpful prod in the right direction".

"Whether you look at the riots last summer, the financial crash and the expenses scandal, or the ongoing terrorist threat from Islamist extremists around the world, one thing is clear: moral neutrality or passive tolerance just isn't going to cut it anymore."

He said people were unwilling to distinguish right from wrong.

"The absence of any real accountability, or moral code, allowed some bankers and politicians to behave with scant regard for the rest of society. And when it comes to fighting violent extremism, the almost fearful passive tolerance of religious extremism that has allowed segregated communities to behave in ways that run completely counter to our values has not contained that extremism but allowed it to grow and prosper."

However emphatic he was about the importance of Christianity to Britain, he was less insistent about its place in his personal life.

As with previous declarations of his belief – once likening it to the patchy reception of a radio station – he told his audience he was a "committed but vaguely practising Church of England Christian" who, while he would stand up for the values and principles" of his faith, was "full of doubts and, like many, constantly grappling with the difficult questions when it comes to some of the big theological issues".